Geodesic
Diagnostics of three-dimensional media by synthesized-aperture methods
Numerical methods and programming, Tome 8 (2007) no. 2, pp. 154-159.

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This paper is devoted to the development of methods and algorithms for solving the inverse problem of wave diagnostics for irregularities in homogeneous media. This inverse problem is considered in a linearized formulation for the Helmholtz equation with an unknown coefficient. A synthesized-aperture method is proposed and an efficient algorithm for solving the inverse problem is developed. A scheme for performing laboratory-scale experiments and the necessary diagnostic equipment for the acquisition of experimental data are also developed. The results of solving the inverse problem with real data of laboratory-scale experiments are discussed. The results obtained demonstrate the high efficiency of our method when applied to experimental data. This work was supported by the Russian Foundation for Basic Research (project 05-01-08068).
Keywords: computer simulation, wave models, inverse problems of wave diagnosis, parallel computing, Helmholtz equation. 
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     author = {G. M. Agayan and N. S. Vinogradov and A. V. Goncharsky and S. L. Ovchinnikov and S. Y. Romanov},
     title = {Diagnostics of three-dimensional media by synthesized-aperture methods},
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     url = {http://geodesic.mathdoc.fr/item/VMP_2007_8_2_a1/}
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G. M. Agayan; N. S. Vinogradov; A. V. Goncharsky; S. L. Ovchinnikov; S. Y. Romanov. Diagnostics of three-dimensional media by synthesized-aperture methods. Numerical methods and programming, Tome 8 (2007) no. 2, pp. 154-159. http://geodesic.mathdoc.fr/item/VMP_2007_8_2_a1/